Enhanced spin Seebeck effect via oxygen manipulation

Spin Seebeck effect (SSE) refers to the generation of an electric voltage transverse to a temperature gradient via a magnon current. SSE offers the potential for efficient thermoelectric devices because the transverse geometry of SSE enables to utilize waste heat from a large-area source by greatly simplifying the device structure. However, SSE suffers from a low thermoelectric conversion efficiency that must be improved for widespread application. Here we show that the SSE substantially enhances by oxidizing a ferromagnet in normal metal/ferromagnet/oxide structures. In W/CoFeB/AlOx structures, voltage-induced interfacial oxidation of CoFeB modifies the SSE, resulting in the enhancement of thermoelectric signal by an order of magnitude. We describe a mechanism for the enhancement that results from a reduced exchange interaction of the oxidized region of ferromagnet, which in turn increases a temperature difference between magnons in the ferromagnet and electrons in the normal metal and/or a gradient of magnon chemical potential in the ferromagnet. Our result will invigorate research for thermoelectric conversion by suggesting a promising way of improving the SSE efficiency.


1-a. Magnon temperature model
We describe the magnon temperature model S1-S4 for an insulator/FM1/FM2/NM structure where the exchange interaction differs between FM1 and FM2 (Fig. S1a, the same as Fig.   1c of the main text). Following Ref. [S4], the equivalent thermal circuit is shown in Fig. S1b.
Here 1 FM ( 2 FM ) is the magnon heat current of FM1 (FM2), 1 FM ( 2 FM ) is the magnon heat resistance of FM1 (FM2), and F2|F1 int ( F1|N int ) is the interface magnon heat resistance at the FM2/FM1 (FM1/NM) interface. Note that the temperature difference between magnons and electrons at the thermal grounds is zero S4 . From the thermal circuit model, we obtain − = which creates a spin accumulation in NM and thus SSE through ISHE. To obtain the ratio SSE1 of SSE with ,1 ≠ ,2 to SSE with ,1 = ,2 , we use the following assumptions. We first assume no loss of magnon heat current at the FM2|FM1 interface (i.e., which is Eq. (3) in the main text.

1-b. Magnon drift-diffusion model
We describe the magnon drift-diffusion model S4,S5 for the same structure of Fig. S1. In FMi (i = 1, 2), a set of drift-diffusion equation for the magnon chemical potential and the magnon spin current is given by S4 where , , and are the magnon diffusion length, the magnon spin conductivity, the spin Seebeck coefficient of FMi, respectively. In NM, a set of drift-diffusion equation for the spin chemical potential and the spin current is given by S4 where , , , and are the spin diffusion length, the charge conductivity, the spin Hall conductivity of NM and the electric field, respectively. The boundary conditions at outer boundaries are: 2 ( = − 2 − 1 ) = ( = ) = 0 . The boundary conditions at the FM2/FM1 interface ( = − 1 ) are: 2 = 1 and 2 = F2|F1 ( 2 − 1 ), where F2|F1 is the interfacial magnon conductance at this interface.
where (= / ) is the spin Hall angle of NM and is the electrode distance to measure SSE . We obtain Eq. (4) with assumptions of continuous magnon chemical potential at the FM2/FM1 interface (i.e., F2|F1 → ∞ ) and 1(2) ≪ 1(2) to simplify SSE . Given ∝ ∝ −1/2 and ∝ 1/2 [S4] (Supplementary Table I), the ratio SSE2 of SSE with ,1 ≠ ,2 to SSE with ,1 = ,2 for the magnon drift-diffusion model is given as which is Eq. (5) in the main text. Here, is the magnon relaxation time related to the Gilbert damping and is the total relaxation time including all scattering processes.

Supplementary Note 2. Numerical calculation of SSE
We use Landau-Lifshitz-Gilbert (LLG) equation for i-th magnetic moment ̂ in 1-D chain along the z axis, where is the gyromagnetic ratio and is the damping parameter of the i-th lattice. The effective field of the i-th lattice is eff, = 2 , (̂− 1 +̂+ 1 ) − 2 ℎ̂+̂ , which consists of the exchange field, easy-plane(xy plane) anisotropy field, and external magnetic field along the +x axis. , is the exchange stiffness of the i-th lattice, is the saturation magnetization, ℎ is the easy-plane anisotropy energy. The thermal fluctuation field th, obeys the Gaussian ensemble S6 , where is the Boltzmann constant, is the temperature of the i-th lattice and is the volume of the ferromagnet unit cell.
To calculate the SSE, we apply a numerical procedure of Ref. [S7]. We calculate the time-  Fig. 2a of the main text, the normal metal layer is in contact to an atomic ferromagnetic layer with the lowest temperature. Therefore, ,1 is the thermal spin pumping current injected to the normal metal, which we focus below.
Oxidation of magnetic materials induces a reduction of Curie temperature and an increase of damping S8 . Reduction of the Curie temperature can be considered as reduction of the exchange stiffness constant. In simulations, therefore, we consider inhomogeneous exchange stiffness or damping within the 1-D atomic chain consisting of 10 lattices. We assume 3 lattices at the hotter region are oxidized and consider the exchange stiffness ( , ) or damping parameters ( ) different from the other 7 lattices (i.e., non-oxidized lattices). Non-oxidized lattices have fixed exchange stiffness and damping parameter as ,0 = 2 × 10 −7 erg cm −1 and 0 = 0.01. We vary these parameters at oxidized lattices as 0.05 ,0 ≤ , ≤ 2 ,0 and 0.05 0 ≤ ≤ 6 0 .

Fig. S2a
shows the result with varying damping parameter in oxidized lattices. ,ℎ is ,1 for the homogeneous case (i.e., = 0 ) whereas , ℎ is ,1 for the inhomogeneous case (i.e., ≠ 0 ). The ratio , ℎ / ,ℎ as a function of / 0 is plotted in the figure. We find that the spin pumping current from the SSE is enhanced (reduced) when the oxidized lattices have a larger (smaller) damping parameter than non-oxidized lattices.
This tendency can be understood by the fluctuation-dissipation theorem stating that the amount of fluctuations must be balanced by the amount of dissipation. In our case, this theorem gives the proportionality of the thermal fluctuation field ℎ to √ . Therefore, an enhanced damping acts like an enhanced temperature for the thermal fluctuations of magnetization. As a result, the enhanced damping in the oxidized region (i.e., the hotter region) increases an effective temperature gradient, which in turn increases the thermal spin pumping current.  The results of Fig. S2 show that both a larger damping parameter and a smaller exchange stiffness in the oxidized lattices enhance the spin pumping current from SSE. However, the damping modulation enhances the spin pumping current only by ~50% even for = 6 0 ( Fig. S2a), which is insufficient to explain the experimental observation. On the other hand, the exchange modulation shows a much larger enhancement of the spin pumping current than the damping modulation (Fig. S2b). Therefore, we attribute the large change in SSE of the experiment to the exchange modulation by oxidation.
The oxidation may also result in changes of the anisotropy or the saturation magnetization.
To check whether these changes can explain our experimental observation, we perform LLG simulation with varying one of these two magnetic properties while fixing other properties (

Figure S3a
shows the result with various ℎ, in oxidized FM lattices. The spin pumping current is found to change within 10 %, compared to that of the homogeneous anisotropy ( ℎ, = ℎ,0 ) case. Therefore, the anisotropy change due to oxidation has no noticeable effect on the SSE. This tendency can be understood by the dominance of exchange interaction over inhomogeneous anisotropy energy in thermal spin pumping. Figure S3b shows the result with various , in oxidized FM lattices. The simulation shows that the spin pumping current is reduced when the oxidized FM lattices have a smaller saturation magnetization than non-oxidized FM lattices. It is a contrary tendency from the experiment. We understand this tendency as a consequence of an enhanced effective exchange field ( = 2 / ) in the oxidized FM lattices. Therefore, varying the anisotropy energy or the saturation magnetization of oxidized FM lattices is unable to describe a largely enhanced SSE due to the oxidation. The oxidation of magnetic materials could also result in a formation of an antiferromagnetic (AFM) phase such as CoO and FeO x at the interface S8 . Therefore, we calculate the spin pumping current for the case that the oxidized lattices have an AFM exchange interaction ( ,0 = −2 × 10 −7 erg cm −1 ). Fig. S4a shows the schematic of SSE calculation with AFM exchange interaction. For 10-lattice system, we vary the number of lattices having the AFM exchange. Each calculation is normalized by ,ℎ with no AFM interaction (= , ). Fig.  S4b shows that the formation of an AFM phase at the hotter region does not enhance the spin pumping current. When the system is fully an AFM phase (the number of AFM couplings = 9), the spin pumping current is found to significantly decrease. This decrease is not meaningful because it originates from the spin-flop transition in the calculation. In summary, a possible formation of AFM phase due to the oxidation cannot explain the experimental observation.

Supplementary Note 3. Magnetic moment changes upon heat treatment
To check that the oxygen migration occurs during the measurement of the temperaturedependent RH, we measured the magnetic moment of the sample before and after heat treatment at 380 K. We used two samples of a W(4 nm)/CoFeB(2 nm)/AlOx(1.5 nm) structure with plasma oxidation times of 0 s and 150 s. Figures S5 a,

electrodes.
We fabricated a Pt, Ta (3 nm)/CoFeB (2 nm)/AlOx (2 nm) structure and examined the VGinduced ΔVTE. Because of the positive spin Hall angle of Pt, the SSE voltage of this sample is expected to be opposite to that of the sample with W ( Figure S6a). VTE was measured while rotating a magnetic field of 100 mT in the x-y plane (azimuthal angle ). Figure S6b shows
Note that we use a Pt electrode with a positive spin Hall angle that makes the ANE and SSE have the same sign in the Pt/CoFeB structure, allowing us to directly compare the magnitude of VTE (ΔVTE) between the samples with different CoFeB thicknesses. Figure S7a shows VTE of the Pt (3 nm)/CoFeB (6 nm)/AlOx (1.5 nm) structure while sweeping an in-plane magnetic field (Bx). The ΔVTE value of the sample is ~ 8.7 μV, which is much larger than that of the Pt (3 nm)/CoFeB (2 nm)/AlOx (1.5 nm) structure (~ 5.4 μV). In addition, we found that the ΔVTE magnitude is further enhanced by increasing the plasma oxidation time from 100 s to 400 s ( Figure S7b), which is consistent with the results in Figure 3 of the main text. We confirm that the main result of our study, the enhancement of TE signal by interfacial oxidation, also works for samples with thicker ferromagnetic materials.

Supplementary Note 6. Estimation of shunting effect
To examine the shunting effect, we first measured the resistivities of the W and CoFeB layers. Figure S8a shows the reciprocal of resistance (R) normalized by the length (L) and width (w) of the sample as a function of the CoFeB thickness (tCoFeB) in the W (4 nm)/CoFeB (tCoFeB)/AlOx (2 nm) structures. From the y-intercept and slope of the linear fit of the graph, the resistivities of W and CoFeB were extracted as 216 Ω•cm and 160 Ω•cm, respectively. We next measured the temperature dependence of R in the W (4 nm)/CoFeB (1 nm)/AlOx (2 nm) structure with different VG of  13 V. Figure S8b shows that the sample with VG = −13 V has a larger R than that with +13 V, which holds over the entire measurement temperature range from 20 K to 380 K. This indicates that more CoFeB is oxidized when negative VG is applied. Note that the weak temperature dependence of R is attributed to the amorphous characteristic of β tungsten S11 .
Assuming that the voltage-induced change in R occurs only in the CoFeB layer, we calculated

Supplementary Note 7. Effect of oxidized FM lattices with larger thermal gradient
The contribution of heat transfer from electrons and phonons to SSE cannot be ignored, particularly given that insulators typically have lower thermal conductivity compared to metals.
This results in a larger thermal gradient for oxidized FM lattices compared to non-oxidized ones. Consequently, the FM oxidation leads to an increase in total SSE not only due to the exchange modulation but also due to the enhanced thermal gradient.
In order to find out which one between the exchange modulation and the enhanced thermal gradient is dominant for the total SSE signal of our experiment, we carry out the following analysis. First, we estimate the SSE enhancement by oxidation from experimental results. Both ANE voltage ANE and SSE voltage SSE contribute to net thermoelectric voltage TE . They are related by a parallel circuit model S12 ; where R [= 1/( F −1 + N −1 )] is the total resistance of FM/normal metal (NM) bilayer and F ( N ) is the resistance of FM (NM).
We estimate ANE from TE data of Ti (3 nm)/CoFeB (2 nm)/AlOx sample assuming no SSE contribution to TE . It is because this sample has a negligible SSE [i.e., a small spin Hall angle of Ti and almost no change in TE at the gate voltage of ±13 V (see Fig. 2f of main text)]. The resistivity of CoFeB is measured to be 160 μΩ • cm (Fig. S9a), which gives CoFeB = 53.3 kΩ (device width w = 15 μm and device length L = 1,000 μm). From the measured total resistance ( Ti/CoFeB = 38.0 kΩ), we obtain Ti = 132.2 kΩ. Using Eq. (S14) and the measured TE (= 13.7 μV; Fig. 2f of main text), we then obtain ANE of 19.2 μV. The gate voltage ( G ) induced SSE enhancement of W (4 nm)/CoFeB (2 nm)/AlOx sample is estimated as follows. W is calculated to be 32.0 kΩ using the measured total resistance ( W/CoFeB = 20.0 kΩ) and CoFeB = 53.3 kΩ. Using Eq. (S14) and TE of W/CoFeB/AlOx sample with G = +13 V (Fig. 2c of main text), we obtain SSE at G = +13 V to be −2.7 μV, which corresponds to the SSE without oxidation. On the other hand, using the same procedure, we obtain SSE at G = −13 V to be −18.4 μV, which is enhanced by oxidation.
Then, the SSE enhancement ratio by oxidation is about 5.8 [= (18.4-2.7)/2.7]. It is noted that we do not consider the oxidation induced reduction in the CoFeB thickness for this estimation.
When we consider this reduction (not shown), the SSE enhancement ratio becomes 5.3.
Therefore, the oxidation of CoFeB results in the SSE enhancement by about five times.
Next, we estimate the SSE enhancement by an increased thermal gradient of oxidized FM lattices. By comparing the resistances of W-based sample at G = ±13 V ( Fig. S9b; device width w = 5 μm, device length L = 35 μm), we estimate the thickness of oxidized CoFeB to be 0.17 nm. We use the heat transfer module of the COMSOL software to calculate the temperature profile of Ru(20)/ZrO 2 (40)/AlO x (2)/CoFeB(2)/W(4)/SiO 2 (100)/SiO in Fig. S10a and Ru(20)/ZrO2(40)/AlOx(2)/CoFeB-oxidized(0.17)/CoFeB(1.83)/W(4)/SiO2(100)/SiO in Fig. 10Sb, where the numbers in parentheses are the thicknesses in the unit of nm. We use parameters of CoOx for the CoFeB-oxidized layer because we can find all parameters necessary for COMSOL simulation for CoOx. A monochromatic 5-μm continuous laser beam of 30 mW is applied on the surface of Ru as in our experiment.
For these Fe-based oxides, we cannot find all parameters necessary for COMSOL simulations so that we estimate the thermal gradient assuming the inverse proportionality of the thermal gradient to the thermal conductivity as this assumption is consistent with our COMSOL simulation [thermal conductivity of CoFeB ( CoFeB ) S13 = 87 W/(m K) -1 , thermal conductivity of CoOx ( CoO x ) S14 = 20 W/(m K) -1 , calculated thermal gradient of CoFeB ( CoFeB ) = Fe3O4, respectively. Overall, therefore, the enhancement of SSE due to the increased thermal gradient of oxides is insufficient to describe the net SSE enhancement (> 500 %) estimated from our measurement. This analysis suggests that the exchange modulation is more dominant for the observed SSE enhancement by oxidation than the increased thermal conductivity.